George Osborne has declared his support for a new runway in the south east of England, possibly at Heathrow airport, and is expected to establish a commission to try and build cross-party support for the controversial move.

In a strategy agreed with the Liberal Democrats, the coalition will uphold its agreement which rules out extra runways at Heathrow, Gatwick and Stansted in this parliament.

Government sources cited the Turner review on pensions and the Browne review on university tuition fees – both established by the Labour government – as examples of commissions set up to find agreement on contentious issues. If agreement was reached, a new runway could be built after the 2015 election.

The move is a reaction to comments from Tim Yeo, the former Tory environment minister, who challenged the prime minister last week to perform a U-turn and support a third runway. Yeo, who changed his position on Heathrow in March, taunted Cameron by writing in the Daily Telegraph: "The prime minister must ask himself whether he is man or mouse."

As MPs prepare to return to Westminster on Monday for a two week pre-conference session, Osborne outlined the government's new thinking on aviation. The chancellor told the Andrew Marr Show on BBC1: "We need more runway capacity in the south east of England. Then there's a question of where it should go – Heathrow, new estuary airport, Stansted, Gatwick. People have lots of different options. What I would say is let's examine all the options; let's do it ... now. Let's make sure we can try and create a political consensus."

Osborne added that, as MP for a Cheshire constituency near Manchester airport, he understood concerns about expanding airports. But he added: "You've got, as a nation, [to] be able to overcome those and make a sensible decision about where that extra runway capacity in the south east should be. What we're going to get ... is a decision that we need new runway capacity and then we're going to seek to achieve a political agreement across the parties on where that should be."

The chancellor's approach is designed to hold the coalition together. The Lib Dems are adamantly opposed to a third runway at Heathrow, unlike Osborne and other senior Tories who believe the case for extra capacity is now overwhelming.

Osborne is also looking to ensure that the transport secretary Justine Greening can remain in the cabinet, if not in the same job. Greening, the MP for Putney, said last week that it would be difficult for her to remain in the cabinet if a third runway were built at Heathrow because she still stands by the Tory pledge at the last election to oppose such a move.

As the government's main political strategist, Osborne also hopes to put pressure on Labour. Ed Miliband came close to resigning as energy and climate change secretary when Gordon Brown insisted on pressing ahead with a third runway. Labour is now opposed to this.

Greening published an aviation strategy document in July which included proposals on emissions, noise levels, night flights and regional airports. An anticipated call for evidence on hub capacity has yet to appear, leaving the new commission to focus on capacity in the south-east.

William Hague confirmed that no decision on an extra runway would be made in this parliament. In an interview on Sky News, the foreign secretary sounded less convinced than Osborne of the need for another runway.

"Everyone will remember that we very clearly said – both coalition parties said in the election campaign – that that's one thing that we wouldn't do and I think it is very important to keep to election promises.

"Sometimes circumstances change so radically, as everybody understands, that that's not possible, but in this case these circumstances have not changed so radically, so it is important to stick to that election promise. It's important to make sure we make the right decision about this and to study all the options, and that is what the government is now going to do."

The Liberal Democrats are still expected to fight the next election on a ticket opposed to a third runway at Heathrow. In a Guardian interview last week Nick Clegg said it was important to preserve the "hub" capacity of Heathrow. But he said this could be achieved by diverting thousands of flights to London's three other airports to free up space for "hub" flights into Heathrow.

It was reported on Sunday that a mystery consortium is drawing up plans for a new, four-runway airport close to Heathrow. The unnamed group of British businesses has commissioned a "world-leading infrastructure firm" to assess potential sites to the west and north of London which could rival – or even replace – Heathrow, according to the Independent on Sunday.

• This article was amended on 3 September 2012. It originally stated that Greening was due to publish an aviation strategy document soon, but it has, in fact, already been published. This has been corrected.